Reliability of researcher capacity estimates and count data dispersion: a comparison of Poisson, negative binomial, and Conway-Maxwell-Poisson models

Item-response models from the psychometric literature have been proposed for the estimation of researcher capacity. Canonical items that can be incorporated in such models to reflect researcher performance are count data (e.g., number of publications, number of citations). Count data can be modeled by Rasch's Poisson counts model that assumes equidispersion (i.e., mean and variance must coincide). However, the mean can be larger as compared to the variance (i.e., underdispersion), or b) smaller as compared to the variance (i.e., overdispersion). Ignoring the presence of overdispersion (underdispersion) can cause standard errors to be liberal (conservative), when the Poisson model is used. Indeed, number of publications or number of citations are known to display overdispersion. Underdispersion, however, is far less acknowledged in the literature. In the current investigation the flexible Conway-Maxwell-Poisson count model is used to examine reliability estimates of capacity in relation to various dispersion patterns. It is shown, that reliability of capacity estimates of inventors drops from .84 (Poisson) to .68 (Conway-Maxwell-Poisson) or .69 (negative binomial). Moreover, with some items displaying overdispersion and some items displaying underdispersion, the dispersion pattern in a reanalysis of Mutz and Daniel's (2018b) researcher data was found to be more complex as compared to previous results. To conclude, a careful examination of competing models including the Conway-Maxwell-Poisson count model should be undertaken prior to any evaluation and interpretation of capacity reliability. Moreover, this work shows that count data psychometric models are well suited for decisions with a focus on top researchers, because conditional reliability estimates (i.e., reliability depending on the level of capacity) were highest for the best researchers.